Based on assumptions of slowly varying envelope approximation and constant polarization state, an intra-optical fiber pulse evolved transmission equation may be described by a nonlinear Schrodinger equation (such as being described by a Manakov equation under random polarization). Such a transmission equation is used to describe waveform evolvement of an optical pulse signal under a combined effect of dispersion and Kerr effect. However, as the nonlinear Schrodinger equation has no analytic solution in taking a combined effect of nonlinearity and dispersion effect, quantitative research on nonlinear damage of an optical fiber and a related theoretical model are being developed and established for approximation solutions of the nonlinear Schrodinger equation.
As it is hopeful that the approximation solutions may reduce calculation complexity of nonlinear analysis, it draws wide attention of the academe and has quickly developed in recent years. As an adaptable method for solving the nonlinear Schrodinger equation, the Volterra series expansion method makes an analysis framework of a conventional communication system to be lent to an optical fiber communication system, and is better for different pulse shapes and link types.
Paolo Serena obtained a regular perturbation (RP) method based on development of the Volterra series expansion method, and granted relatively definite physical meanings to the orders or perturbation, thereby making the method for solving the nonlinear Schrodinger equation developed rapidly, and various theoretical frameworks being derived for quantifying nonlinear distortion in the time domain or the frequency domain. A generalized result shows that for a typical long-haul optical fiber transmission system, a nonlinear action is fully described by Volterra series under three orders (one order of perturbation), therefore, the currently popular nonlinear analysis accepts an analysis framework of the Volterra series expansion of a lower order, i.e. quasi-linear approximation. In the quasi-linear approximation, a one-order perturbation framework for solving a nonlinear transmission equation may be summarized as solving a vector sum of a pulse after dispersion (linear) action subjected to nonlinear distortion at every points in a propagation path, which is analytically expressed as that a product of time domain three items for transmission of the pulse is a triple integral of the integrand.
Theoretic analysis shows that an analytic expression of one-order perturbation may be simplified under certain conditions, such that calculation complexity of a perturbation method may be reduced. Currently, a most typical and successful theoretical approximation is an analytic solution of a lossless large dispersion link, and in such a method, it is assumed that the optical fiber transmission link is lossless and the accumulated dispersion is sufficiently large, and a carrier pulse for transmitting a digital sequence is ensured to be in a Gaussian shape. In the above approximation, the triple integral of the one-order perturbation may be strictly integrable, which may be expressed as a closed-form solution of a special function. Although such a method may reduce the calculation complexity to a large extent, as key Gaussian pulse approximation exists, precision of calculation in a non-Gaussian pulse transmission system that is relatively widely used is limited, thereby limiting a range of application of this method.
As the mature of high-speed digital signal process (DSP) and narrowband optical filtering technologies, attention is paid more and more to optical orthogonal frequency division multiplexing (OOFDM) technology with a high spectral utilization and Nyquist wave division multiplexing (Nyquist WDM) technology. In a transmission system with a high spectral utilization, as a spectral density of signals is further enlarged, nonlinear damages are intensified, thereby resulting in comparable negative effect on power budget and transmission distance of the system. In such a scenario, in order to achieve more accurate coherent transmission system performance estimation and find out more optimal system design rules, study on accurate nonlinear theoretical models are outstandingly meaningful.
It should be noted that the above description of the background is merely provided for clear and complete explanation of the present disclosure and for easy understanding by those skilled in the art. And it should not be understood that the above technical solution is known to those skilled in the art as it is described in the background of the present disclosure.
Documents advantageous to the understanding of the present disclosure and the prior art are listed below, which are incorporated herein by reference, as they are fully described herein.
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